• [1]

    Kazunori Akiyama et al., Astrophys. J. Lett. 875, L1 (2019), arXiv: 1906.11238

  • [2]

    Kazunori Akiyama et al., Astrophys. J. Lett. 875(1), L2 (2019), arXiv: 1906.11239

  • [3]

    Kazunori Akiyama et al., Astrophys. J. Lett. 875(1), L3 (2019), arXiv: 1906.11240

  • [4]

    Kazunori Akiyama et al., Astrophys. J. Lett. 875(1), L4 (2019), arXiv: 1906.11241

  • [5]

    Kazunori Akiyama et al., Astrophys. J. Lett. 875(1), L5 (2019), arXiv: 1906.11242

  • [6]

    Kazunori Akiyama et al., Astrophys. J. Lett. 875(1), L6 (2019), arXiv: 1906.11243

  • [7]

    Kazunori Akiyama et al., Astrophys. J. Lett. 910(1), L12 (2021), arXiv: 2105.01169

  • [8]

    Kazunori Akiyama et al., Astrophys. J. Lett. 910(1), L13 (2021), arXiv: 2105.01173

  • [9]

    Kazunori Akiyama et al., Astrophys. J. Lett. 930(2), L12 (2022)

  • [10]

    Kazunori Akiyama et al., Astrophys. J. Lett. 930(2), L13 (2022)

  • [11]

    Kazunori Akiyama et al., Astrophys. J. Lett. 930(2), L14 (2022)

  • [12]

    Kazunori Akiyama et al., Astrophys. J. Lett. 930(2), L15 (2022)

  • [13]

    Kazunori Akiyama et al., Astrophys. J. Lett. 930(2), L16 (2022)

  • [14]

    Kazunori Akiyama et al., Astrophys. J. Lett. 930(2), L17 (2022)

  • [15]

    J. L. Synge, Mon. Not. Roy. Astron. Soc. 131(3), 463 (1966)

  • [16]

    James M. Bardeen, William H. Press, and Saul A Teukolsky, Astrophys. J. 178, 347 (1972)

  • [17]

    J. M. Bardeen. Timelike and null geodesics in the Kerr metric. In Les Houches Summer School of Theoretical Physics: Black Holes, 1973.

  • [18]

    K. S.Virbhadra and George F. R. Ellis, Phys. Rev. D 62, 084003 (2000), arXiv: astro-ph/9904193

  • [19]

    Clarissa-Marie Claudel, K. S. Virbhadra, and G. F. R. Ellis, J. Math. Phys. 42, 818 (2001), arXiv: gr-qc/0005050

  • [20]

    K. S. Virbhadra, Phys. Rev. D 79, 083004 (2009), arXiv: 0810.2109

  • [21]

    Valerio Bozza, Gen. Rel. Grav. 42, 2269 (2010), arXiv: 0911.2187

  • [22]

    K. S. Virbhadra, Phys. Rev. D 106(6), 064038 (2022), arXiv: 2204.01879

  • [23]

    Leonardo Amarilla, Ernesto F. Eiroa, and Gaston Giribet, Phys. Rev. D 81, 124045 (2010), arXiv: 1005.0607

  • [24]

    Leonardo Amarilla and Ernesto F. Eiroa, Phys. Rev. D 85, 064019 (2012), arXiv: 1112.6349

  • [25]

    Shao-Wen Wei and Yu-Xiao Liu, JCAP 11, 063 (2013), arXiv: 1311.4251

  • [26]

    Farruh Atamurotov, Sushant G. Ghosh, and Bobomurat Ahmedov, Eur. Phys. J. C 76(5), 273 (2016), arXiv: 1506.03690

  • [27]

    Sara Dastan, Reza Saffari, and Saheb Soroushfar. Shadow of a Charged Rotating Black Hole in f(R) Gravity. 6 2016. arXiv: 1606.06994.

  • [28]

    Mingzhi Wang, Songbai Chen, and Jiliang Jing, JCAP 10, 051 (2017), arXiv: 1707.09451

  • [29]

    Dimitry Ayzenberg and Nicolas Yunes, Class. Quant. Grav. 35(23), 235002 (2018), arXiv: 1807.08422

  • [30]

    Zdenek Stuchlík and Jan Schee, Eur. Phys. J. C 79(1), 44 (2019)

  • [31]

    Liang Ma and H. Lu, Phys. Lett. B 807, 135535 (2020), arXiv: 1912.05569

  • [32]

    Minyong Guo, Shupeng Song, and Haopeng Yan, Phys. Rev. D 101(2), 024055 (2020), arXiv: 1911.04796

  • [33]

    Tao Zhu, Qiang Wu, Mubasher Jamil, and Kimet Jusufi, Phys. Rev. D 100(4), 044055 (2019), arXiv: 1906.05673

  • [34]

    Tian-Chi Ma, He-Xu Zhang, Peng-Zhang He, Hao-Ran Zhang, Yuan Chen, and Jian-Bo Deng, Mod. Phys. Lett. A 36(17), 2150112 (2021), arXiv: 2010.00151

  • [35]

    Zezhou Hu, Zhen Zhong, Peng-Cheng Li, Minyong Guo, and Bin Chen, Phys. Rev. D 103(4), 044057 (2021), arXiv: 2012.07022

  • [36]

    S. I. Kruglov, Mod. Phys. Lett. A 35(35), 2050291 (2020), arXiv: 2009.07657

  • [37]

    Shao-Wen Wei and Yu-Xiao Liu, Eur. Phys. J. Plus 136(4), 436 (2021), arXiv: 2003.07769

  • [38]

    Xiao-Xiong Zeng, Hai-Qing Zhang, and Hongbao Zhang, Eur. Phys. J. C 80(9), 872 (2020), arXiv: 2004.12074

  • [39]

    Minyong Guo and Peng-Cheng Li, Eur. Phys. J. C 80(6), 588 (2020), arXiv: 2003.02523

  • [40]

    Ming Zhang and Jie Jiang, Phys. Rev. D 103(2), 025005 (2021), arXiv: 2010.12194

  • [41]

    Zhen Zhong, Zezhou Hu, Haopeng Yan, Minyong Guo, and Bin Chen, Phys. Rev. D 104(10), 104028 (2021), arXiv: 2108.06140

  • [42]

    Andrea Addazi, Salvatore Capozziello, and Sergei Odintsov, Phys. Lett. B 816, 136257 (2021), arXiv: 2103.16856

  • [43]

    Aoyun He, Jun Tao, Peng Wang, Yadong Xue, and Lingkai Zhang, Eur. Phys. J. C 82(8), 683 (2022), arXiv: 2205.12779

  • [44]

    Pedro V. P. Cunha, Emanuele Berti, and Carlos A. R. Herdeiro, Phys. Rev. Lett. 119(25), 251102 (2017), arXiv: 1708.04211

  • [45]

    Bakhtiyor Narzilloev, Javlon Rayimbaev, Sanjar Shaymatov, Ahmadjon Abdujabbarov, Bobomurat Ahmedov, and Cosimo Bambi, Rev. D 102(4), 044013 (2020), arXiv: 2007.12462

  • [46]

    Minyong Guo and Sijie Gao, Phys. Rev. D 103(10), 104031 (2021), arXiv: 2011.02211

  • [47]

    Carlos A. R. Herdeiro, Alexandre M. Pombo, Eugen Radu, Pedro V. P. Cunha, and Nicolas SanchisGual, JCAP 04, 051 (2021), arXiv: 2102.01703

  • [48]

    Vitor Cardoso, Edgardo Franzin, and Paolo Pani. Is the gravitational-wave ringdown a probe of the event horizon? Phys. Rev. Lett., 116(17): 171101, 2016.[Erratum: Phys.Rev.Lett. 117, 089902 (2016)]. arXiv: 1602.07309, doi: 10.1103/PhysRevLett.116.171101.

  • [49]

    Zachary Mark, Aaron Zimmerman, Song Ming Du, and Yanbei Chen, Phys. Rev. D 96(8), 084002 (2017), arXiv: 1706.06155

  • [50]

    Pablo Bueno, Pablo A. Cano, Frederik Goelen, Thomas Hertog, and Bert Vercnocke, Phys. Rev. D 97(2), 024040 (2018), arXiv: 1711.00391

  • [51]

    R. A. Konoplya, Z. Stuchlík, and A. Zhidenko, Phys. Rev. D 99(2), 024007 (2019), arXiv: 1810.01295

  • [52]

    Yu-Tong Wang, Jun Zhang, and Yun-Song Piao, Phys. Lett. B 795, 314 (2019), arXiv: 1810.04885

  • [53]

    Yu-Tong Wang, Zhi-Peng Li, Jun Zhang, Shuang-Yong Zhou, and Yun-Song Piao, Phys. J. C 78(6), 482 (2018), arXiv: 1802.02003

  • [54]

    Vitor Cardoso and Paolo Pani, Living Rev. Rel. 22(1), 4 (2019), arXiv: 1904.05363

  • [55]

    José T. Gálvez Ghersi, Andrei V. Frolov, and David A. Dobre, Class. Quant. Grav. 36(13), 135006 (2019), arXiv: 1901.06625

  • [56]

    Hang Liu, Peng Liu, Yunqi Liu, Bin Wang, and Jian-Pin Wu, Phys. Rev. D 103(2), 024006 (2021), arXiv: 2007.09078

  • [57]

    Yi Yang, Dong Liu, Zhaoyi Xu, Yujia Xing, Shurui Wu, and Zheng-Wen Long, Phys. Rev. D 104(10), 104021 (2021), arXiv: 2107.06554

  • [58]

    Min-Yan Ou, Meng-Yun Lai, and Hyat Huang. Echoes from Asymmetric Wormholes and Black Bounce. 11 2021. arXiv: 2111.13890.

  • [59]

    Vittorio De Falco, Emmanuele Battista, Salvatore Capozziello, and Mariafelicia De Laurentis, Phys. Rev. D 101(10), 104037 (2020), arXiv: 2004.14849

  • [60]

    Vittorio De Falco, Mariafelicia De Laurentis, and Salvatore Capozziello, Phys. Rev. D 104(2), 024053, 6 (2021), arXiv: 2106.12564

  • [61]

    Xiaobao Wang, Peng-Cheng Li, Cheng-Yong Zhang, and Minyong Guo, Phys. Lett. B 811, 135930 (2020), arXiv: 2007.03327

  • [62]

    Maciek Wielgus, Jiri Horak, Frederic Vincent, and Marek Abramowicz, Phys. Rev. D 102(8), 084044 (2020), arXiv: 2008.10130

  • [63]

    Merce Guerrero, Gonzalo J. Olmo, and Diego Rubiera-Garcia, JCAP 04, 066 (2021), arXiv: 2102.00840

  • [64]

    Jun Peng, Minyong Guo, and Xing-Hui Feng, Phys. Rev. D 104(12), 124010 (2021), arXiv: 2102.05488

  • [65]

    Merce Guerrero, Gonzalo J. Olmo, Diego Rubiera-Garcia, and Diego Gómez Sáez-Chillón, Phys. Rev. D 105(8), 084057 (2022), arXiv: 2202.03809

  • [66]

    Carlos A.R. Herdeiro, Eugen Radu, Nicolas Sanchis-Gual, and José A. Font, Phys. Rev. Lett. 121(10), 101102 (2018), arXiv: 1806.05190

  • [67]

    Peng Wang, Houwen Wu, and Haitang Yang, Phys. Rev. D 103(10), 104012 (2021), arXiv: 2012.01066

  • [68]

    Qingyu Gan, Peng Wang, Houwen Wu, and Haitang Yang, Phys. Rev. D 104(2), 024003 (2021), arXiv: 2104.08703

  • [69]

    Guangzhou Guo, Peng Wang, Houwen Wu, and Haitang Yang, Eur. Phys. J. C 81(10), 864 (2021), arXiv: 2102.04015

  • [70]

    Guangzhou Guo, Peng Wang, Houwen Wu, and Haitang Yang, Phys. Rev. D 105(6), 064069 (2022), arXiv: 2107.04467

  • [71]

    Guangzhou Guo, Peng Wang, Houwen Wu, and Haitang Yang, JHEP 06, 073 (2022), arXiv: 2204.00982

  • [72]

    Qingyu Gan, Peng Wang, Houwen Wu, and Haitang Yang, Phys. Rev. D 104(4), 044049 (2021), arXiv: 2105.11770

  • [73]

    Guangzhou Guo, Xin Jiang, Peng Wang, and Houwen Wu, Phys. Rev. D 105(12), 124064 (2022), arXiv: 2204.13948

  • [74]

    G. Witzel et al., Astrophys. J. 917(2), 73 (2021), arXiv: 2011.09582

  • [75]

    Joseph M. Michail, Mark Wardle, Farhad Yusef-Zadeh, and Devaky Kunneriath, Astrophys. J. 923(1), 54 (2021), arXiv: 2107.09681

  • [76]

    R. Abuter et al., Astron. Astrophys. 654, A22 (2021), arXiv: 2107.01096

  • [77]

    J. Dexter et al., Mon. Not. Roy. Astron. Soc. 497(4), 4999 (2020), arXiv: 2006.03657

  • [78]

    Nicolas Scepi, Jason Dexter, and Mitchell C. Begelman, Mon. Not. Roy. Astron. Soc. 511(3), 3536 (2022), arXiv: 2107.08056

  • [79]

    I. El Mellah, B. Cerutti, B. Crinquand, and K. Parfrey, Astron. Astrophys. 663, A169 (2022), arXiv: 2112.03933

  • [80]

    Roberto Abuter, A Amorim, M Bauböck, JP Berger, H Bonnet, W Brandner, Y Clénet, V Coudé Du Foresto, PT de Zeeuw, C Deen, et al., Astronomy & Astrophysics 618, L10 (2018)

  • [81]

    M. Bauböck et al., Astron. Astrophys. 635, A143 (2020), arXiv: 2002.08374

  • [82]

    Maciek Wielgus, Monika Moscibrodzka, Jesse Vos, Zachary Gelles, Ivan Marti-Vidal, Joseph Farah, Nicola Marchili, Ciriaco Goddi, and Hugo Messias, Astron. Astrophys. 665, L6 (2022), arXiv: 2209.09926

  • [83]

    Jiewei Huang, Zhenyu Zhang, Minyong Guo, and Bin Chen. Images and flares of geodesic hotspots around a Kerr black hole. 2 2024. arXiv: 2402.16293.

  • [84]

    Yiqian Chen, Peng Wang, and Haitang Yang, Eur. Phys. J. C 84(3), 270 (2024), arXiv: 2401.10905

  • [85]

    Zilong Li and Cosimo Bambi, Phys. Rev. D 90, 024071 (2014), arXiv: 1405.1883

  • [86]

    João Luís Rosa, Paulo Garcia, Frédéric H. Vincent, and Vitor Cardoso, Phys. Rev. D 106(4), 044031 (2022), arXiv: 2205.11541

  • [87]

    Yiqian Chen, Peng Wang, Houwen Wu, and Haitang Yang, Journal of Cosmology and Astroparticle Physics (04), 032 (2024)

  • [88]

    Alex Simpson and Matt Visser, JCAP 02, 042 (2019), arXiv: 1812.07114

  • [89]

    J. R. Nascimento, A. Yu. Petrov, P. J. Porfirio, and A. R. Soares, Phys. Rev. D 102(4), 044021 (2020), arXiv: 2005.13096

  • [90]

    Haroldo C. D. Lima, Junior., Luís C. B. Crispino, Pedro V. P. Cunha, and Carlos A. R. Herdeiro, Phys. Rev. D 103(8), 084040, 2 (2021), arXiv: 2102.07034

  • [91]

    Kirill A. Bronnikov, Roman A. Konoplya, and Thomas D. Pappas, Phys. Rev. D 103(12), 124062 (2021), arXiv: 2102.10679

  • [92]

    Naoki Tsukamoto, Phys. Rev. D 103(2), 024033 (2021), arXiv: 2011.03932

  • [93]

    Rajibul Shaikh, Kunal Pal, Kuntal Pal, and Tapobrata Sarkar, Mon. Not. Roy. Astron. Soc. 506(1), 1229 (2021), arXiv: 2102.04299

  • [94]

    M. Cvetic, G. W. Gibbons, and C. N. Pope, Phys. Rev. D 94(10), 106005 (2016), arXiv: 1608.02202

  • [95]

    Pedro V. P. Cunha, Carlos A. R. Herdeiro, Eugen Radu, and Helgi F. Runarsson, Int. J. Mod. Phys. D 25(09), 1641021 (2016), arXiv: 1605.08293

  • [96]

    Andy Bohn, William Throwe, Fran Hébert, Katherine Henriksson, Darius Bunandar, Mark A. Scheel, and Nicholas W. Taylor, Quant. Grav. 32(6), 065002 (2015), arXiv: 1410.7775

  • [97]

    Pedro V. P. Cunha, Carlos A. R. Herdeiro, Eugen Radu, and Helgi F. Runarsson, Phys. Rev. Lett. 115(21), 211102 (2015), arXiv: 1509.00021

  • [98]

    Yiqian Chen, Peng Wang, Houwen Wu, and Haitang Yang. Gravitational Lensing by Born-Infeld Naked Singularities. 5 2023. arXiv: 2305.17411.

  • [99]

    Deyou Chen, Yiqian Chen, Peng Wang, Tianshu Wu, and Houwen Wu. Gravitational Lensing by Transparent Janis-Newman-Winicour Naked Singularities. 9 2023. arXiv: 2309.00905.

  • [100]

    Yiqian Chen, Peng Wang, and Haitang Yang. Observations of Orbiting Hot Spots around Naked Singularities. 9 2023. arXiv: 2309.04157.

  • [101]

    N. Hamaus, T. Paumard, T. Muller, S. Gillessen, F. Eisenhauer, S. Trippe, and R. Genzel, Astrophys. J. 692, 902 (2009), arXiv: 0810.4947

  • [102]

    João Luís Rosa, Caio F. B. Macedo, and Diego Rubiera-Garcia, Phys. Rev. D 108(4), 044021 (2023), arXiv: 2303.17296

  • [103]

    Hanna Liis Tamm and João Luís Rosa, Phys. Rev. D 109(4), 044062, 10 (2023), arXiv: 2310.12681

  • [104]

    João Luís Rosa, Daniela S. J. Cordeiro, Caio F. B. Macedo, and Francisco S. N. Lobo. Observational imprints of gravastars from accretion disks and hot-spots. 1 2024. arXiv: 2401.07766.